In recent years, there have been proposed and developed various automotive continuously variable transmissions (CVTs), for example, belt-drive continuously variable transmissions or toroidal continuously variable transmissions. In either a belt-drive CVT or a toroidal CVT, a speed ratio is controlled and varied responsively to a vehicle running state. For instance, a belt-drive CVT employs a primary variable-width pulley, a secondary variable-width pulley, and a drive belt (i.e., a segmented steel belt) running in the pair of variable-width pulleys. The CVT is configured such that torque, inputted from an internal combustion engine to the primary pulley, is transmitted via the drive belt to the secondary pulley, while steplessly varying a transmission ratio (in other words, a torque ratio) by changing the effective diameters of the primary and secondary pulleys. A shift control apparatus of the CVT is configured to utilize a shift characteristic diagram stored in a memory of a CVT control unit and set or preprogrammed based on simulations and experiments. Shift control is executed in accordance with a selected one of shift lines (shift patterns) defined by the shift characteristic diagram. For instance, in the case of a belt-drive CVT, a target primary-pulley rotational speed is set or determined, based on both the accelerator opening (the accelerator pedal position) and the vehicle speed, from a preprogrammed shift characteristic diagram. A target transmission radio (a target pulley ration) is determined based on the set target primary-pulley rotational speed. Then, shift control is executed by controlling the pulley groove width of each of the primary and secondary pulleys so that the actual pulley groove widths of the primary and secondary pulleys are brought into respective target pulley groove widths, corresponding to the determined target transmission ratio. On some shift control apparatus of CVTs, a CVT control unit is configured to determine, based on a driver's accelerator-pedal operation or a driver's accelerator manipulated variable (e.g., an accelerator pedal position changed by the driver and/or a driver's accelerator depression speed), whether or not there is a driver's intention to accelerate. When it is determined that a driver's intention to accelerate is present, switching from a normal shift line to a shift line suited for vehicle acceleration occurs, and thus a target transmission ratio is set or determined based on the shift line suited for vehicle acceleration. One such shift control apparatus of the CVT has been disclosed in Japanese Patent Provisional Publication No. 2005-164000 (hereinafter referred to as “JP2005-164000”).